You want to take advantage of the inserted logical table that is available in the context of a trigger. It matches the schema for the table that is being inserted to and includes the row(s) that will be inserted (in an update trigger you have access to the inserted and deleted logical tables which represent the the new and original data respectively.)
So to insert Employee / Department pairs that do not currently exist you might try something like the following.
CREATE TRIGGER trig_Update_Employee
ON [EmployeeResult]
FOR INSERT
AS
Begin
Insert into Employee (Name, Department)
Select Distinct i.Name, i.Department
from Inserted i
Left Join Employee e
on i.Name = e.Name and i.Department = e.Department
where e.Name is null
End